Biomechanical Considerations for Striking Implements - Background
• Relationship between linear motion and rotary motion– Radius of rotation– Axis of rotation
• Relationship between torque and rotational motion– Moment of Inertia: I = mk2
– Radius of gyration: k = (I/m).5
– Rotational analogues of newton’s laws: T = I• Elastic properties of striking implements
– Coefficient of restitution– Vibrations during the swing (bending)– Vibrations during and after impact
• Sweet spot determinants– Center of percussion, vibrational nodes
Relationship between linear and angular motion
• Would you rather have a long or short baseball bat or golf club? Why?
What is Moment of Inertia (MOI)?
Here, r (the radius of rotation) is equal to k (the radius of gyration), but that is not the case with extended bodies
It is the resistance of a system to rotational acceleration, and is calculated at follows:
What is radius of gyration (k)?
An indicator of distribution of massabout the axis. It is the distance fromthe axis to a point at which all themass of a system of equal masswould be concentrated to have the MOI equal the original system. Itis, then, the average weighted distance of the mass of a systemto the axis.
Equivalent systems
k 35
k 35
Determining MOI & K • Simple 3-segment system:
– I = mi di2 = m1 d1
2 + m2 d22+
m3 d32 + . . . . . . .+ mi di
2
– I = mk2 ; k = (I/m).5
• Irregularly shaped bodies
But we can’t measure all of these small masses!
Physical pendulum properties (rigid bodies)
• Radius and axis of rotation
• Radius of gyration (K)
• Moment of inertia (MOI)
• Center of percussion
Physical pendulum method of determining MOI and K
• Suspend object at axis• Measure mass (m), and distance from axis to COM, r• Measure period of oscillation (T)
– Moment of inertia (I) = T2 mr * .248387 m/sec
– Radius of gyration (K) = ( I/m).5
Semi-rigid (elastic) bodies)•Coefficient of restitution
•Vibrations - nodes and modesVibrations when bat is clamped (during swing )
Vibrations when bat is free(during impact with ball)
Coefficient of Restitution (COR)• COR is a measure of the liveliness of an object
• When 2 objects collide:
• When one object is stationary,
this reduces to:
• An alternative way to measure COR
• Is to drop a ball and measure the ht
• Bounced compared to ht dropped:
Coefficient of Restitution (COR)• COR of balls dropped or thrown at a rigid wooden
surface is shown here.
• COR increases
directly with
temperature and
inversely with
impact velocity.
Questions
• What is the sweet spot of a striking implement?
• How do we take advantage of rigid body properties to improve implement?
• How do we take advantage of elastic properties to improve implement?
Evaluation methods for striking implements
• Apply scientific principles to evaluate mfgr claims • Use it yourself, if possible• Product reviews on the internet & in trade mags• Consult with others who use it, or supervise its use• Consult with professors, or professionals (e.g., coaches)
with specialized insight and expertise• Look at research available, if any
– Evaluate quality of research – • Extrinsic - who is sponsoring the research, where did it appear?
• Intrinsic – methods, procedures, statistics, conclusions
Next: Bats & Clubs• Tuesday, November 1
– Lecture on golf clubs – Read Ch 9 of Kreighbaum and Smith– Submit 2 questions related to readings on golf clubs
• Thursday, November 3– Guest Speaker: Chris Hay, Golf USA
• Tuesday, November 8– Lecture on softball and baseball bats – Read Ch 10 of Kreighbaum & Smith– Submit 2 questions relating to readings on bats
• Thursday, November 10– Review new bat products
• 2005 catalogues from leading bat manufacturers• Bats from lab
• Review for exam